The trend of the next generation of the internet has already been scrutinized by top analytics enterprises. According to Gartner investigations, it is predicted that, by 2024, 75% of the global population will have their personal data covered under privacy regulations. This alarming statistic necessitates the orchestration of several security components to address the enormous challenges posed by federated and distributed learning environments. Federated learning (FL) is a promising technique that allows multiple parties to collaboratively train a model without sharing their data. However, even though FL is seen as a privacy-preserving distributed machine learning method, recent works have demonstrated that FL is vulnerable to some privacy attacks. Homomorphic encryption (HE) and differential privacy (DP) are two promising techniques that can be used to address these privacy concerns. HE allows secure computations on encrypted data, while DP provides strong privacy guarantees by adding noise to the data. This paper first presents consistent attacks on privacy in federated learning and then provides an overview of HE and DP techniques for secure federated learning in next-generation internet applications. It discusses the strengths and weaknesses of these techniques in different settings as described in the literature, with a particular focus on the trade-off between privacy and convergence, as well as the computation overheads involved. The objective of this paper is to analyze the challenges associated with each technique and identify potential opportunities and solutions for designing a more robust, privacy-preserving federated learning framework.